Whole-Brain Evaluation of Cortical Microconnectomes

Abstract The brain is an organ that functions as a network of many elements connected in a nonuniform manner. In the brain, the neocortex is evolutionarily newest and is thought to be primarily responsible for the high intelligence of mammals. In the mature mammalian brain, all cortical regions are expected to have some degree of homology, but have some variations of local circuits to achieve specific functions performed by individual regions. However, few cellular-level studies have examined how the networks within different cortical regions differ. This study aimed to find rules for systematic changes of connectivity (microconnectomes) across 16 different cortical region groups. We also observed unknown trends in basic parameters in vitro such as firing rate and layer thickness across brain regions. Results revealed that the frontal group shows unique characteristics such as dense active neurons, thick cortex, and strong connections with deeper layers. This suggests the frontal side of the cortex is inherently capable of driving, even in isolation and that frontal nodes provide the driving force generating a global pattern of spontaneous synchronous activity, such as the default mode network. This finding provides a new hypothesis explaining why disruption in the frontal region causes a large impact on mental health.


Introduction
The brain is an organ with very nonuniformly connected components working together as a network.Extracting any systematic rule about such nonuniformity in terms of internal characteristics of local components may provide important insights about how the brain processes information in parallel across different scales, such as cellular scale and anatomic scale.

Focus on cortex
Within the brain, the neocortex is an evolutionary novelty and an important component of the brain that supports the high intelligence of mammals, including humans (Kaas, 2020).
At first glance, in the neocortex, roughly similar circuits are arranged throughout the entire cortical sheet.However, although there is some degree of similarity, there is also a certain degree of uniqueness (DeFelipe et al., 2002;Nelson, 2002;Douglas and Martin, 2004).In fact, in the brain of a mature animal, each cortical region is assigned a distinct set of functions.To perform different functions, individual brain regions must either receive different inputs from the outside via the inter-regional connections or/and have different local circuits within them.Inter-regional similarities and differences of cortical microcircuits In the past, detailed comparisons of the structure of local circuits in different regions have been mainly made among a few cortical areas (Nelson, 2002).It has been suggested that cortical local circuits share a common design and constitute a "canonical circuit" (Douglas et al., 1989;Miller, 2016).At the same time, each region also has a distinct profile of connectivity (Harris and Shepherd, 2015;De Biase and Bonci, 2019;Batiuk et al., 2020).In other words, each area can have systematic differences according to the spatial distances and topological distances of their connections (DeFelipe, 2002;Wang, 2020).
Corroborative evidence has come from comparisons of cell density and cortical thickness in several regions (Fulcher et al., 2019).Studies in the broader mammalian species have also shown that cell density varies across cortical regions, a finding that is being rapidly elucidated not only by classical immunostaining (Collins et al., 2010;Herculano-Houzel et al., 2013;Keller et al., 2018), but also by emerging transparency techniques (Hama et al., 2011;Chung et al., 2013;Susaki et al., 2014).Systematic rules for the relationship between connections between brain regions and cell density are also becoming clearer (Herculano-Houzel et al., 2013;Shimono, 2013).
Despite the widespread interest and substantial volume of research in this field, there still exist few global and quantitative comparisons across different brain regions on how information is internally exchanged among .100neurons in local neural circuits, based on experimental data.In particular, there are almost no studies that have made a wide comparison between brain regions, stepping into the topological differences in functional connectivity.Therefore, if we can extract the rules of "differences among individual brain regions," such information is expected to be a source of significant benefits not only for brain modeling but also for, in a wide range of aspects such as contrast with other nonuniformity indicators, understanding of disease states, etc.
Approaches to exploring the topology of connections between hundreds or more neurons have evolved into a research field called the microconnectome (Schröter et al., 2017).Our past studies have also focused on a single brain region to study the microconnectome, and have repeatedly evaluated and improved the technology (Shimono and Beggs, 2014;Nigam et al., 2016;Kajiwara et al., 2021).
This present study extended the technique to all cortical regions of the mouse, and evaluated how each cortical brain region differs especially in terms of the topologies of functional local circuits, and other basic physiological parameters, such as firing rate and layer thickness.Specifically, we conducted an analysis focusing on the prefrontal cortex.This is because the prefrontal cortex forms networks with other brain regions and controls the flow of information, enabling adaptive behaviors.For instance, it regulates various cognitive processes such as information integration, decision-making, planning, and behavioral inhibition (Miller and Cohen, 2001;Bicks et al., 2015;Fuster, 2015).Similar regions to the prefrontal cortex are also found in mice, suggesting that certain higher-order cognitive functions are regulated in mice as well (Uylings et al., 2003).Thus, investigations into the specificity of the prefrontal cortex in mice are being conducted from both cross-species and speciesspecific perspectives (Morishima and Kawaguchi, 2006;Carlén, 2017).Then, we evaluated density and functional interconnections from active neurons, something that cannot be captured by applying staining technique to dead brain slices.

Physiologic experiments
The present study acquired acute brain slices from 16 groups of cortical regions of the cerebral cortex and simultaneously measured electrical activity from a large number of neurons within the brain slices (Fig. 1a; Table 1).The experimental protocols we employed, which included 3D scanning, immunostaining, and electrical activity measurements, were consistent with those outlined in previously published studies.These protocols, including detailed explanations, have been demonstrated in a video journal (Ide et al., 2019;Kajiwara et al., 2021;Shirakami et al., 2022).All animal experiments were performed according to animal experiment protocols approved by the Kyoto University Animal Committee.All mice used were female C57BL/6J mice (n ¼ 37, three to five weeks old, n ! 2 per group).
The thickness of the cortical slices was 300 mm, and we used a multielectrode array (MEA) system (Maxwell Biosystem, MaxOne) for simultaneous measurement of electrical activity.During the measurements, we refluxed an artificial CSF (ACSF) solution saturated with 95% O 2 /5% CO 2 .
Also, we performed spike sorting (Spyking Circus software) on the time series obtained from the electrical measurements to identify ;1000 neurons; the short distance spacing between the electrodes of the MEA system (15 mm) allows us to estimate the spatial position of the neurons very accurately.The parameters used in the spike sorting were the same as those in Kajiwara et al. (2021).
Before and after the electrical measurements, we measured 3D scans of the brain surface (Ide et al., 2019), and by comparing and superimposing the scan data with the magnetic resonance (MR) images recorded before the brain was extracted, we were able to accurately define the slice positions of individual brain regions with less than one slice resolution (Fig. 1a).

Connectivity estimation and E/I categorization
In this study, after classifying neurons into inhibitory and excitatory, we estimated the presence or absence of connections and calculated the strength of connections for each neuron type.It is important to note that the classification of neurons must be done before determining connectivity, since the shuffled null data and the real data for excitatory and inhibitory synaptic connections must be compared separately.Transfer entropy (TE) is used to estimate connectivity (connected or not) and sorted local transfer entropy (SLTE) is used to classify neurons into inhibitory/excitatory (E/I), a further modification on transfer entropy.The method used in this study is basically based on the method previously (Kajiwara et al., 2021).The source code is also available on GitHub (https://github.com/ShimonoMLab).
TE used for connectivity estimation is a type of method to evaluate information transfer between different variables beyond false correlations and confounding factors (Okatan et al., 2005;Fig. 2b).Relationship between structure and function (Honey et al., 2007;Hlavá cková et al., 2009;Ito et al., 2011;Stetter et al., 2012;Timme et al., 2016), topology consistent with patch-clamp experiments, the presence of hubs and modules (Shimono andBeggs, 2014, 2015), are successfully demonstrated that Figure 1.Scheme of the whole analysis.a, An example of a mouse brain magnetic resonance (MR) images.We cut out acute slices at the location of the lines, and measured electrical activity from them, and then immunostained them.b, An example of immunostaining.The cortical area surrounded by black circles indicates the area where electrophysiological measurements were also performed.c, Electrophysiological measurements provide a time series of spikes in the activity of hundreds of neurons.d, From the time series, directional interactions were inferred and effective networks were constructed.We evaluated not only basic physiological metrics but also various metrics of the effective networks.Extended Data Figure 1-1 provides additional information for this figure.
Table 1: Definition of 16 regional groups, and number of mice used for individual groups Estimation of E/I categories and intercellular connections from spike data.a, Example of spike data displayed as a raster plot.Neurons i and j were extracted from this large number of neurons.b, Then, the influence of other neuron j on the main neuron i was evaluated by transfer entropy.The effects of the combination of the activity state of neuron i at delay 0 and the activity state of neuron j at delay d on the TE and SLTE values were summarized in a table with positive and negative values.The magnitude of the effect was expressed as "big" or "small."c, TE was obtained as a function TE(d) that depends on delay, and from TE(d), the peak value strength and the peak sharpness were calculated.The value of SLTE at the delay where TE takes the peak was also extracted.d, Flowchart describing the overall flow of cell categorization and connectivity estimation after the SLTE and TE are prepared.
Step 1: the E-I bias matrix was obtained from the peak SLTE values, from which the E-I category for each neuron was determined.
Step 2: strength and Sharpness were obtained as a matrix from the TE values for all combinations of neurons.
Step 3: the matrix was classified into four connection types based on the E-I categories.Step4: finally, the presence or absence of connections and the strength of the connections were obtained by comparing them to the shuffled data for each of those categories.
distributions of connection weights are close to logarithmic (Nigam et al., 2016).
In other words, TE has its advantages both with respect to theoretical formulations and the requirements imposed by physiological data (Lizier et al., 2008;Vicente et al., 2011;Wibral et al., 2013).
In addition, SLTE, used to classify neurons into inhibitory and excitatory, is a measure like transfer entropy (TE), but sorts local transfer entropy according to the positive and negative signs of the different interactions (Lizier et al., 2008).Because it sorts by positive and negative sign, SLTE can distinguish excitatory and inhibitory interactions of presynaptic spike events relative to postsynaptic spike events using the opposite sign of the local transfer entropy of excitatory and inhibitory interactions (Lizier et al., 2008;Goetze and Lai, 2019).

More information about connectivity estimation
The transfer entropy (TE) used for connection estimation measures the extent to which the prediction accuracy of the activity of neuron i is improved by including information on the spiking activity of neuron j, compared with prediction accuracy based solely on the past of neuron i (Fig. 2a).The equation for TE used in this study is expressed as follows: This equation quantifies the expected value of the local transfer entropy log p i t ji tÀ1 ; j tÀd À Á p i t ji tÀ1 À Á ! for all i tÀ1 , j tÀd and i t (Schreiber, 2000).The variables i or j are given the index of time to express if neuron i or j is active or not at a time bin.The values are 1 when they are spiking, and 0 when they are not spiking.The size of the time bin was set to 1 ms, which is common for spiking data, and we evaluated the degree of improvement in prediction accuracy when the t À d ms time bin of neuron j was used in addition to the t À 1 ms time bin of neuron i to predict the state of the most recent t ms time bin of neuron i (Fig. 2b).This is because it was demonstrated that, for neuron j, the inclusion of multiple past time bins does not significantly alter prediction accuracy as a function of TE(d) (Shimono and Beggs, 2015;Nigam et al., 2016;Fig. 2c).
When there is direct interaction because of synaptic connections from neuron j to neuron i, TE(d) shows a strong and sharp peak (Berry and Pentreath, 1976).Here, Strength is defined as the peak value of TE(d), so TEðd peak Þ, and Sharpness is defined by the following equation (Fig. 2c; Shimono and Beggs, 2015;Nigam et al., 2016;Kajiwara et al., 2021): d¼0 TEðdÞ

:
(2) Here, the range of the denominator of Sharpness in Equation 2 is set to 30 ms as the time window as the sufficient length of time window for electrical signals to transmit in the spatial size of the brain region (1 Â 2 mm) we record (Mason et al., 1991;Swadlow, 1994;Shimono and Beggs, 2015), and the numerator is calculated using the standard deviation of time delays between the spike of a presynaptic neuron and the subsequent spike of a postsynaptic neuron across all neuron pairs, with a set t value of 4 ms.
From this raw data, we created a shuffled spike array by swapping the spikes of presynaptic neurons into spikefree bins within 610 ms (Fig. 2d; Hatsopoulos et al., 2003).The TE obtained from it is called TE shuffle j!i , and the TE obtained from the original data are called TE real j!i .Then, by comparing the raw connectivity matrix with the connectivity matrix generated from the 100 shuffled spike series, we selected the connections with strong and sharp peaks in TE(d) on the Strength-Sharpness space.Here, we shuffled uniformly across the entire 30-ms time window.In this study, we used the same threshold as in Kajiwara et al., 2021 to determine the connections, and the connection probability was expressed as a median and standard deviation, resulting in 2.8 6 3.3%.
The connection strength was defined as IT j!i ¼ TE real j!i À TE shuffle j!i for the shuffled data.This connection strength has been repeatedly evaluated by comparing it to EPSPs measured by patch clamp recordings (Shimono andBeggs, 2014, 2015).See previous studies for details (Shimono and Beggs, 2015;Nigam et al., 2016;Kajiwara et al., 2021).

More information about cell categorization
The mathematical definition of the sorted local transfer entropy (SLTE) used to classify neurons into inhibitory/excitable (E/I) is as follows: In SLTE, the local transfer entropy is weighted differently by the multiplier ðÀ1Þ ði t Àj tÀd Þ .Depending on whether the events of each neuron i and j are spiking or inactive, i t and j t-d will be 1 or 0. Therefore, this multiplier is 11 when i t and j t-d are both the same event and À1 when they are different events (Fig. 2b).As a result, in the case of an excitatory interaction, the local transfer entropy is added, and in the case of an inhibitory interaction, the local transfer entropy is subtracted.This reordering rule results in the sum of all terms being positive for excitatory interactions and negative for inhibitory interactions.Note that in this quantification, for example, the amount of information given by p i tÀ1 ¼ 0; j tÀd ¼ 1 ð Þ for a rare event i t ¼ 1 is much larger than that given by p i tÀ1 ¼ 1; j tÀd ¼ 1 ð Þ for a frequent event i t ¼ 0 (Fig. 2b).
To emphasize the time window where direct synaptic influence is evident, we selected SLTE values with a time delay d in which TE exhibits a peak value (Fig. 2c).In the subsequent sections, the peak SLTE value will simply be referred to as the E-I bias.
Then, after removing the bottom 10% of the absolute value of the E-I bias to ensure a high signal-to-noise ratio, the E-I bias value was sorted to calculate the remaining top 90% of E-I bias, which was derived from the output side for each transmitting neuron separately based on the order of the peak TE values, TE nor , normalized to account for the effect of firing rate.
In the two-dimensional space of this sum and the logarithm of the per-neuron firing rate, we identified relevant clusters using hierarchical clustering based on the Ward variance minimization algorithm and assigned excitatory labels to neurons belonging to clusters that were relatively common and on the positive side of the SLTE sum, which is naturally predicted from the Dale's principle (Dale, 1934).
In Kajiwara et al. (2021), we verified that the classification performance of this method is also high for computational models and in vivo data; we confirmed that similar classification performance can be obtained with SLTE alone, but in the end, the firing rate is the second axis, considering that the combination of SLTE alone gives slightly better classification performance than SLTE alone.
As a final summary, we list how the TE-based connection estimation and SLTE-based neuron classification can be combined as the following four steps procedures (Fig. 2d).
Step 1: first, from the SLTE, neurons are classified into excitatory and inhibitory neurons through the E-I bias matrix.
Step 2: next, from the TE, the strength matrix (a matrix of peak intensities relative to delay) and the sharpness matrix (a matrix of peak sharpness relative to delay) are computed.
Step3: the two matrices were then decomposed into four categories: excitatory-excitatory, excitatory-inhibitory, inhibitory-excitatory, and inhibitory-inhibitory.Step 4: finally, connectivity and connection strength were determined using shuffled null data for each of the four connection types.In this process, we partition the two-dimensional space of Sharpness and connection strength into a grid.We then identify the regions where the sample size of the original data exceeds that of the shuffled data by a certain proportion as the connected areas.Please refer to Kajiwara et al. (2021) for more detailed information.

MRI acquisition
This study measured 3D T-weighted (T2W) images of the whole brain in each mouse.For this purpose, a 7T, 210-mm horizontal bore, preclinical scanner (BioSpec 70/20 USR, Bruker BioSpin MRI GmbH) MR system equipped with a 440 mT/m, 100-ms ramp time gradient system was used for relaxation enhancement (RARE) sequence was used; for RF excitation and signal reception, an orthogonal volume resonator [35 mm of inner diameter (i.d.), T9988; Bruker BioSpin] was used.
We also used a protocol called TurboRARE-3D (Bruker BioSpin), and the specific acquisition parameters are as follows: repetition time (TR) 2000 ms; echo time (TE) 9 ms; effective TE 45 ms; RARE factor 16; acquisition matrix size 196 Â 144 Â 144; field of view (FOV) 19.6 Â 14.4 Â 14.4 mm; acquisition bandwidth 75 kHz, axial (coronal direction in scanner setting): bandwidth 2.6-ms Gaussian p /2 pulse for fat suppression and spoiler gradient with 1051-Hz bandwidth, two dummy scans, averaging number 3, acquisition time 2 h 42 m, excitation pulse 2.59 ms, re-convergence pulse 1.94 ms, pulse shape: p /2 pulse, bandwidth 1051 Hz, fat suppression averaging number was 3. Pulse shape was sinc3, bandwidth was 2400 Hz.The software for the measurements was ParaVision 5.1.The cortical surface images were extracted from the measured MRI images using FSL.For details, see Ide et al. (2020).

Slice preparation and electrophysiological recording
In this study, we recorded neuronal spikes from neocortical slices using the multielectrode array (MEA) system.For this purpose, mice were first sufficiently anesthetized with 1À1.5% isoflurane, then transferred a cortical slice to a Petri dish (100 Â 20 mm) containing ice-cold cutting solution with air flow containing 95% O 2 and 5% CO 2 .The extracted brain was cut into two blocks and then sliced into two to five slices (300 mm thick) in a diagonal angle to the cortical surface using a vibratome (Neo Linear Slicer NLS-MT; DOSAKA EM CO., LTD).
We selected cutting speed, frequency, and swing width as 12.7 mm/min, 87-88 Hz, and 0.8-1.0mm, respectively, and slowed the speed down if the brain needed to be cut carefully for a temporary period.
All slices analyzed in this study were taken orthogonal to the cortical surface in any region (Fig. 1b).The angle cutting slices was carefully chosen, and the coordinates of the sections, including anterior-posterior coordinates and hemispheres, were recorded in a format when the brain sections were cut, and the slices were also reconfirmed and accurately recorded by embedding them within the MRI space acquired during the MR measurements described above (Ide et al., 2019).
The slices were incubated for 1 h in a beaker filled with prewarmed ACSF (;34°C), then we selected one slice per animal and moved with a thick plastic pipette onto the MEA array and positioned the slice with a soft brush to record properly from a specific brain region including the cortex.The MEA array is rectangular in shape (2.0 Â 4.0 mm), with 26,000 electrodes uniformly distributed (Fig. 1c) and the distance between adjacent electrodes was 15 mm (Maxwell Biosystem, MaxOne; https://www.mxwbio.com/).
Before the main electrical recording, a so-called prescan of 30 (s) was performed by recordings from adjacent 1020 sensors combinationally covering the all sensors, and up to 1020 sensor sensors that responded more strongly than 0.03 mV and more frequently than 0.1 Hz were selected.
The main electrical recording of spontaneous neural activity from the selected sensors was then performed for ;2.5 h.In our experimental setting, the firing rate did not decay in this 2.5 h.Indeed, in vitro slice measurements with such prolonged recording times are rare.This long recording is an important factor in achieving high performances of connectivity estimation (Extended Data Fig. 1-1, right side panels, comparing ranked firing rates between 1/4-2/4 and 3/4-4/4 of the time series).
During this prescan and main measurements, the slices were still perfused at 1 ml/min with ACSF that was saturated with 95% O 2 /5% CO 2 while controlling the temperature of the perfusate around 34°C.

Brain surface scan
We recorded the brain surface in three different 3D scans: the whole brain immediately after extraction, the brain block cut into two blocks, and the brain block remaining after slicing into slices.For each object, the brain itself is measured at least twice, flipping up and down as needed.In addition, between one measurement from the same object, 16 images are scanned by rotating the object.For its 3D scanning, a scanning system based on 3D structural optical technology (SCAN in a BOX; Open Technologies) was used (Besl and McKay, 1992).Before scanning, it is extremely important to lightly wipe the brain surface with a microfiber cloth to prevent diffuse reflections (Ide et al., 2020).The scanned images were processed using the 3D scanning and processing software IDEA (including SCAN in a BOX).
First, the automatic alignment option of that IDEA was used to correct small disagreements between its 16 images and integrated them.The merged image was obtained for the number of times it was recorded from the same object.
Next, the merged images were superimposed and merged using the manual alignment option.The optimization algorithm was an iterative closest point (ICP) algorithm without nonlinear deformation, which is often applied to rigid 3D objects (Besl and McKay, 1992).After scanning, all scan planes were verified to be nicely overlapped.
Third, a high-resolution meshed object was created from the merged objects using the mesh generation option, saved in stl-binary format, and superimposed on the mesh image of the brain surface obtained from the individual MRI images using IDEA.
By the normalization process of FSL, the cross-sections of the superimposed brain slices are grouped together in the same normalized brain space (Extended Data Fig. 1-1a).

Immunohistochemistry staining
The cerebral cortex has a "Baumkuchen"-like pattern of six overlaid sheets in the depth direction.Physiologically, each of these sheets are called layers.The layers are named layers 1-6 in order from the surface of the brain toward its depth.The layer architecture could be visually observed by immunostaining using NeuN and GAD.
To acquire information on cortical layers, immunohistochemical staining was performed in the 3 d after MEA recordings were completed; overnight after MEA measurements, brain slices were fixed with 4% paraformaldehyde (PFA) in PBS at 4°C.
On the next day (day 1), the same slices were washed with PBS for 5 min three times in total, and then incubated with antigen activating solution (10 mM sodium citrate, pH 6.0) for 20 min at 95-98°C.Then, after cooling it to room temperature (20-25°C), the slices were washed with 1% Na bisulfite in 50 mM Tris-buffered saline and incubated with blocking solution for 2 h at room temperature.The blocking solution is a solution prepared by adding 4% normal goat serum (NGS) and 0.5% octylphenol ethoxylate (Triton X-100) to a 1% Na bisulfite-Tris solution (pH 7.5).After washing with 1% Na bisulfite in 50 mM Tris-buffered saline, the slices were incubated with the blocking solution for 2 h at room temperature.The slices were then soaked in a primary antibody solution consisting of 1:800 mouse anti-GAD67 and 1:500 rabbit anti-NeuN and incubated overnight at 4°C.The primary antibody solution was prepared by diluting the primary antibody with 1% NGS and 0.5% Triton X-100 in 1% Na bisulfite-Tris solution.
On the second day, the same slices were replaced in a secondary antibody solution.The secondary antibody solution is a solution prepared by diluting a secondary antibody consisting of 1:500 goat anti-mouse and 1:500 goat anti-rabbit with Tris-NaCl solution (8.5 g/l NaCl in 50 mM Tris-buffered saline, pH 7.5) and Tris-NaCl with 3% NGS and 0.3% Triton X-100.Then, the slices were washed a total of three times for 5 min in Tris-NaCl solution and incubated overnight at 4°C.
On the third day, after washing a total of four times for 5 min in Tris-NaCl solution, the slices were placed on glass slides, embedded with antifade reagent (SlowFade Gold; Invitrogen), surrounded with coverslips, and then examined from the slides with a fluorescence microscope (All-in-One Fluorescence Microscope BZ-X710; Keyence) to record cell body distribution at 10Â and 20Â magnifications.

Extracting layer categories
We applied Image processing consisting of three steps to the given fluorescence images (Kajiwara et al., 2021).Please refer the previous report in detail.Here, we briefly explain the method to define layer categories.
First, after applying noise removal preprocessing to the NeuN image, the cell bodies were identified using the Watershed algorithm.Here, the boundaries between neurons (including overlapping neurons) were first detected by drawing an estimated contour line that gradually increases from the centers toward the cell surfaces.From those detected boundaries, the centers of the neurons can also be defined.
Second, the number of neurons identified was divided by the spatial size of 50 Â 50 pixels to calculate the density distribution.Along the depth direction, which is perpendicular to both the surface and the bottom of the cortex, a histogram proportional to the cell density was obtained.This was accomplished by summing the number of neurons in each bin along the direction perpendicular to the cortical layer.
Third, the layers are defined based on the density distribution of neurons.The neuron density distribution generally showed three convex points corresponding to the centers of layers 3, 4, and 6, and two concave points between those convex points.For that distribution, all boundaries were defined in the following three steps.(1) Between the cortical surface and the first convex point, we defined the boundary between layers 1 and 2 as the 1/3 point between the cortical surface and the first convex point, and the boundary between layers 2 and 3 as the 2/3 point between the cortical surface and the second convex point.(2) Next, the boundary between layers 3 and 4 was defined at the concave point between the first and second convex points.(3) Finally, the boundary between the layers 4 and 5 was defined at the midpoint between the second convex point and the second concave point, and the boundary between the layers 5 and 6 was defined at the midpoint between the second and third concave points.In this study, layers 2-6 are discussed because layer 1 protruded from the measuring region of some samples in the electrical measurement.

Overlaying between a staining image and a MEA map
Next, we assigned layer labels to neurons derived from the electrophysiology by overlaying the layer boundaries obtained from the above image analysis on top of the multielectrode arrays.
In this procedure, first, the cortical layer boundaries obtained from the stained images were superimposed on the unstained images (photographic images taken immediately after MEA recording; Fig. 1e).Then, typical points (10 points on the cortical surface, seven points on the cortical base, and other additional points) common to the stained and unstained images were selected.Based on the iterative nearest neighbor algorithm (Greenspan and Godin, 2001), an optimal mapping of those typical points resulted in a transformation matrix from the stained image to the unstained one, which was then multiplied to the coordinates of the stained image to overlap the two images.
Second, to superimpose the unstained image onto the MEA coordinates, the four corners of the unstained image were selected, and a transformation matrix was obtained that optimally overlapped the MEA coordinates and the four points of the unstained image.By multiplying the inverse of the transformation matrix by the MEA coordinates, the layer boundaries obtained from the stained image were superimposed on the MEA, and layer labels were assigned to individual neurons (Extended Data Fig. 1-1b, left panels).In the subsequent analysis in this study, only the cortical areas were extracted and included in the analysis.This has the effect of reducing unexpected noise in the analysis of spiking data from neurons from outside of the cortex.

Network metrics Degree
Degree is a metric defined for each node and is the number of edges connecting to each node.In a directed graph with oriented edges, there are incoming edges and outgoing edges, so two indices, in-degree and out-degree, are defined for each type vertex.The in-degree is the number of edges coming into the vertex, and the outdegree is the number of edges going out from the vertex.The distribution of frequencies of vertices with similar degrees is called degree distribution and is frequently used to characterize structure of networks.

Weight
Weight refers to the strength of the connection, and here it is calculated by normalizing the amount of information calculated from the real spike data by the amount of information obtained when the time sequence of the spikes is shuffled.In other words, weight assesses the rate at which firing between two neurons occurs causally within a few milliseconds.
Past studies have reported that this metric shows statistically similar trends to synaptic connections (Song et al., 2005;Nigam et al., 2016;Kajiwara et al., 2021).It should be noted that if one neuron outputs more neurons, the amount of information sent to the individual destination neurons is smaller.

k-Core
Next, we used the k-Core index as another representative measure of centrality along with degree (Seidman, 1983).k-Core is determined by removing a node with zero connections (isolated vertex) to a node with one connection, to a node with two connections, and so on from the original connection structure.In general, a k-Core is defined as a partial network that consists only of nodes that (1) remain after removing nodes of order less than k, and (2) have a number of connections greater than k.To define k-Core in consideration of both rules (1) and ( 2), it should be noted that a k-Core does not necessarily correspond to a network that consists that of only nodes with degrees greater than or equal to k in many cases.

Feedback vertex set
A set of nodes in a directed graph (or network) is called a feedback vertex set (FVS) if removal of the incoming edges to the set eliminates all directed cycles.It is known that for reasonably wide classes of linear and nonlinear systems, statically and periodically steady states of the whole network are determined by specifying states of the nodes in an FVS (Akutsu, et al., 1998;Mochizuki et al., 2013).
The minimum feedback vertex set (MFVS) is the FVS with the minimum number of nodes and can be regarded as a minimum set of driver nodes.However, MFVS may not be uniquely determined in many cases.In order to cope with this issue, the weighted minimum FVS (WMFVS) was introduced by making use of weights assigned to nodes, where WMFVS is the MFVS with the maximum total node weight (Li et al., 2021).Recall that the weight of a node is defined as the sum of edge weights (connection strength) incoming to the nodes.Therefore, it is expected that WMFVS is uniquely determined if various weights are assigned to the nodes.Although computation of both MFVS and WMFVS is theoretically difficult (NP-hard), these can be computed efficiently for moderate size networks by using integer linear programming (Li et al., 2021).

Results
We aimed to compare the differences in functional networks between neurons in brain regions.Before that, we also compared basic physiological or anatomic metrics such as age, cortical thickness, and neuron densities.Therefore, we divided the brain into 16 circumferential categories based on the rotating angle as shown in Figure 3a, and defined abbreviated names as listed in Table 1.In this article, we simply call the 16 individual brain region categories as given names based on the angle.

Basic metric 1: age
Since the neuron density, firing rate, and network architecture are likely to change at different ages, it is necessary to measure all data for the same age group to simply compare between brain regions.
First of all, we show the age of individuals included in the 16 circumferential categories (Fig. 3b).The average age of each category shows that they are almost stable at around four weeks old (three to five weeks).

Basic metric 2: layer thickness
Next, we observed some basic anatomic or physiological indices according to two steps.First, we compared the cortical thickness among the eight categories for individual hemispheres (Fig. 3b).Previous studies reported that cortical regions categorized as frontal group (or group F in our definition) are thicker than other regions (Grand'maison et al., 2013;Pagani et al., 2016).
Therefore, we performed the following statistical tests, hypothesizing that two to three adjacent brain regions around the frontal group would also show differences compared with other regions.
Here, we found a trend that the cortical thickness was higher in an adjacent pair of brain regions, categorized into the frontal and frontal dorsal groups, than other remaining seven groups (p , 0.005, Mann-Whitney test,  1 refers to these definitions of abbreviation names.In the following seven panels, the left hemisphere corresponds to the left half of the circle, and the right hemisphere to the right half.b, This panel summarizes ages of mice used in individual experiments.Lines show the averages of the data within each of the 16 categories.(The left and right hemispheres are expressed with yellow-green and cyan colored lines, respectively.)Black points show the age of each individual mouse used in this experiment.c, represents the thickness of all layers of the cortex, the line is the average value for each angle, and red dots express raw data.In addition to the panel c, panels d-h express the thickness of individual layers (layers 2, 3, 4, 5, 6) separately.The pie chart regarding layer thickness is represented as a bar graph in Extended Data Figure 3-1.The data for cortical thickness are stored in Extended Data Table 3-1.groups F and FD).This trend was commonly observed between two hemispheres.
Second, we extended this finding further by observing the thickness of individual layers (Fig. 3c-h).Here, we found layer four was observed to be thinnest on the dorsal side, which corresponds to the motor cortex.This finding was also consistent with arguments from previous studies that stated layer four is not prominent in many regions, for example, the motor cortex (García-Cabezas and Barbas, 2014;Yamawaki et al., 2014).
More interestingly, this trend of selectively increasing thickness in the F and FD groups is common across the many layers [layers 2-5, p , 0.05, Mann-Whitney test, effect size .0.5, sample sizes: (9,28)], except in the deepest layer [layer 6, p .0.05, Mann-Whitney test, sample sizes: (9,28)].Here, the statistical test was performed based on the same hypothesis for the case of all layers.We will discuss this new finding in the discussion section.Here, we performed a nonparametric test comparing the cortical thickness of the LF, LFV, RF, and RFV layers with that of the other 12 groups as the reference.Notice that we always used Mann-Whitney test corrected with Bonferroni's corrections.

Basic metric 3: density of active neurons
Next, we observed the neuron density.Density of active neurons is calculated by dividing the number of neurons with a firing rate .0.1 Hz by the recording area of the region where the neurons were present, but not divided by the thickness, 300 mm.We call the density of active neurons simply as "neuron density" in this report.
Here, notice that we produced acute slices that were orthogonal, and not tangential, to the brain surface.Therefore, the thickness of the cortex could correspond with one axis of our electrode array.Besides, we defined E/I (excitatory or inhibitory) categories for individual neurons based on properties of output connections of the neurons (Kajiwara et al., 2021).Therefore, we could calculate the density of active excitatory and inhibitory neurons by dividing the numbers of identified excitatory or inhibitory neurons by the spatial size covering a region of focus.Here, we put slices on a rectangular recording region to keep the cortical surface closely in parallel with one axis of the recording region.Therefore, for simplicity, we were also able to qualitatively use cortical thickness as the normalization factor instead of the size of the recording cortical region.
As mentioned before, we hypothesized that a few groups near the frontal region should be the main target of the statistical test to compare with other groups.This hypothesis was further supported by the observation that the frontal region exhibited a distinct cortical thickness.
Then, for the density of active excitatory neurons for all layers, frontal and frontal ventral regions showed significantly higher values than other regions [p-value ¼ 0.0419 , 0.05, effect size ¼ 0.63, sample sizes: (9,23), Mann-Whitney test].
Additionally, we performed a separate analysis of the individual layers defined based on immunostaining.The results showed that the trend of nonuniformity of density of active excitatory neurons was completely different between superficial and deep layers.Specifically, in deep layer 5 or 6, the high density around the frontal side was pronounced [layers 2-4, p .0.05, sample sizes: (9,27)], while, in deeper layers, the high density around the frontal side was not so strongly observed [layer 5, p , 0.05, p ¼ 0.035, effect size ¼ 0.58, sample sizes: (9,27); layer 6, p-value ¼ 0.015 , 0.05, F and FV, effect size ¼ 0.67, sample sizes: (9,27), Mann-Whitney test].Briefly speaking, the trend, that the density of active excitatory neurons is high around the frontal side was observed for all layers, but the trend was much stronger trend observed in the deep layers.

Basic metric 4: E/I balance
We aimed to explore the differences between cortical layers in addition to obtaining a distinction between excitatory and inhibitory neurons.
Past studies have shown that E/I balance is fairly stable and distributed in different areas of the cortex (Moreau et al., 2010;Xue et al., 2014).We quantified E/I balance as the ratio between numbers of active excitatory neurons and inhibitory neurons to the number of all active neurons.In fact, although the E/I ratio was stable (Fig. 4m), we observed that in the superficial layers, the neuron density of active neurons was higher in the occipital to dorsal occipital regions, whereas in the deeper layers, especially layer 6, the neuron density of active neurons tended to be higher in the frontal side.Notice that, in subsequent text, the "neuron density of active neurons" will be referred to simply as "active neurons."Finally, we observed the firing rate in each brain region (Fig. 4g-l).This information beyond structural features is especially important because it is information that cannot be observed from dead slices by staining etc.
Surprisingly, although the firing rate of inhibitory neurons was basically higher than excitatory neurons, a bimodal peak in the firing rate of excitatory neurons was observed around the dorsal (LD, RD) and (occipital) ventral (LOV, RV) regions in both hemispheres.And after performing a statistical test between excitatory and inhibitory neurons, selecting the vicinity of the peaks as target, the firing rate of inhibitory neurons was not significantly greater than that of excitatory neurons [corrected p .0.05, excitatory vs inhibitory neurons within dorsal and ventral groups, Mann-Whitney test, effect size: 0.74, sample sizes: (8,8)].
Up to this section, we have considered the properties of individual neurons.However, we also need to understand neurons as a network system, in which neurons essentially function by their mutual interactions.Therefore, from the next section, we start to analyze the topological properties as connected networks of nodes, neurons.

Network metric 1: degree centrality
In order to move beyond the single neuron level, we will now explore several widely-used network measures (Fig. 5a,b).The degree centrality, a basic measure of how central a neuron is among possible paths within a network, was relatively higher in inhibitory neurons than in excitatory neurons in most of the regions, in terms both of in-degree and out-degree (in-degree: corrected p-value ¼ 0.90, all regions, out-degree: p ¼ 0.50, all regions).Tables 4-1 and 4-2.It has been shown in previous studies that inhibitory neurons are functionally connected to more neurons than excitatory neurons in the somatosensory region (Kajiwara et al., 2021), and a similar trend could be observed at occipital regions (LOD, ROD, LO, RO).Current observation revealed that whether inhibitory or excitatory neurons show higher degree centrality largely depends on the cortical region observed.

Network metric 2: k-Core centrality
In order to check whether the tendency observed with degree centrality can be shown with a different centrality metric, we also observed k-Core centrality (Fig. 5c).The radar chart of the k-Core of excitatory neuron groups showed that the value at the frontal side (RF, RFV, LF, LFV) is slightly larger than in other regions [corrected p-value ¼ 0.16, Mann-Whitney test corrected by Bonferroni's method, effect size: 0.60, sample sizes: (9,28)].The following statistical tests are also corrected by the Bonferroni's method.

Network metric 3: controlling ability
Next, we used the feedback vertex set (FVS) index to measure the ability of inhibitory and excitatory cells to control other cells in each local circuit of the brain region.FVS provides a kind of measure of the ability of a neuron to change the intensity of its output while monitoring the surrounding situation by looping its own effects on other cells and returning to oneself.
Here, we will briefly explain how to calculate the FVS.In a directed network that can be written with arrows, we focus on a group of nodes.When removal of all incoming connections to the nodes in the group eliminates all directed cycles, the node group is called the feedback vertex set (FVS).
Furthermore, the FVS with the smallest number of nodes is called the minimum feedback vertex set (MFVS).Nodes in MFVS can be considered as driver nodes, and thus we can compare the control ability of the inhibitory neurons and the excitatory neurons by counting the number of MFVS nodes contained in each class of neurons.In our previous study, we evaluated the somatomotor region alone and found that inhibitory cells showed higher controlling ability than excitatory cells (Kajiwara et al., 2021).However, MFVS may not be determined uniquely.Therefore, in this study, we employed the weighted minimum FVS (WMFVS), which is the MFVS with the maximum total node weight, where the weight of a node is defined as the sum of edge weights (see below) incoming to the nodes.
In this study, somatomotor regions belong to LFD or RFD.As a result of this cortical wide-area evaluation, it became clear that the dominance of inhibitory to excitatory neurons' controlling ability shows wide variety among regions (Fig. 5d).Here, we could observe relatively higher control ability of inhibitory neurons than excitatory neurons at LO, LOD, ROD, RO [corrected p-value ¼ 0.40, Mann-Whitney test, corrected by Bonferroni's method, effect size: 0.45, sample sizes: (8,8)].

Network metric 4: weight
Weight is the strength of the connection.All observations up to this point were unweighted (not considering connection strength).And in those observations, the values for inhibitory neurons relatively more often exceeded those for excitatory neurons.We obtained the strength from the amount of information calculated from the spike data using a calculation procedure that shows properties similar to synaptic strength (Song et al., 2005;Nigam et al., 2016).
These regions are basically the frontal cortex.Recall that the activity quantified with firing rate was strongest in the motor cortex (or somatosensory cortex), which was slightly more dorsal (or occipital) than these areas.Because current experimentally observed targets are segmented cortical slices, the projecting targets of individual neurons must exist within the observed region.This experimental setting means that the connection strength is defined as mainly and essentially the strength of connections within individual cortical regions.Therefore, simply speaking, we expect that the strong connection within a brain region leads to a strong firing rate at the same brain regions.However, the real resultsdemonstrated that the areas where strong connections were observed did not necessarily have a high firing rate.
Next, to observe the connections between different layers in more detail, we shifted to the observation as a weighted matrix where the horizontal and vertical axes are the indices of the layers.

Network metric 5: interlayer weighted networks
We then observed the connection strengths (connection weights) observed in metric 4, grouped by layer.That is, the connection strength from each of layers 2-6 to each of layers 2-6 was represented as a single matrix for each region.In the individual color maps, the x-axis is for layers where the neurons sending out connections belong, and the y-axis is for layers where the neurons receiving connections belong.As a total, we were able to draw similar connection matrices from 16 regions for the left and right hemispheres (Fig. 6b), and the angles of 16 maps correspond to the angle used in other figures shown so far.
Furthermore, we conducted an evaluation of the connection strength for all combinations of regions concerning connections from the sixth layer (Fig. 6c-e).To provide a comprehensive assessment, we adopted the Network-Based Statistics (NBS) permutation test (Zalesky et al., 2010).In this test, the significance of the actual data are evaluated by comparing the t statistic of the real data with that of data obtained from random shuffling.This permutation process was repeated 10,000 times.Additionally, we calculated the effect size using the difference in means between the two samples.
As a result, we observed that p-values, particularly centered around frontal regions like LFV, LF, and RFV, and also in LOV, ROV, and RF, were significant in some cases (Fig. 6c,d).Upon examining the effect size, we found that among the significant regions, especially frontal areas like LFV, LF, RF, and RFV, showed relatively higher values (Fig. 6e).Although significant regions were visible in the vertical lines for ROV, the effect size was not observed to be particularly high.
From the above perspectives, we also attempted to test between the frontal and frontal ventral regions and other areas.As a result, in the sixth layer of the frontal and frontal ventral regions, we observed that both of output connections from sixth layers [corrected p-value ¼ 2.4 Â 10 À4 , Mann-Whitney test, effect size: 0.68, sample sizes: (60,156)] and input connections to sixth layers [corrected p-value ¼ 0.040, Mann-Whitney test, effect size: 0.45, sample sizes: (24,72)] are stronger than the other layers in the frontal and frontal ventral regions which are located around the left and right edges of the figure (Fig. 6b, yellow regions).
Incidentally, in the NBS test, the tendency for significance to appear consolidated in the frontal region was observed in other layers as well.This suggests that in the frontal region, it does not appear to be a characteristic specific to the deeper layers.This point is further shown in Extended Data Figure 6-2.

Discussion
In the Results section, we have observed differences among several cortical regions for each single metric.Now we consider the same results from a different perspective.Specifically, the results were reinterpreted by grouping the various metrics observed from the perspective of individual brain regions.

Main findings
In this study, we conducted observations focusing on the frontal group.It has been reported in the past that cortical thickness is greater in this frontal region than in other regions (Fulcher et al., 2019).Furthermore, on observing the thickness of the cortex in separate layers, we found that the trend was observed in the superficial layer thicknesses but not in the deep layer ones.
It was also known in the past that the somatosensory cortex and frontal region are areas with high neuron density, following the visual cortex (Herculano-Houzel et al., 2013;Keller et al., 2018).We also separately observed neuron density by layers.As a result, the layer with significantly highest density in the frontal region was the deeper layer, while the visual cortex showed the highest density in the superficial layers.
In the counting of the number of neurons detected by staining, the neuron density was greatest in the visual cortex.However, in our results, the neuron density in the frontal cortex might exceed that in the visual cortex because we counted the sufficiently active neurons detected by our electrical activity measurement.In fact, the density of active neurons will not correspond with simple neuron density.
Interestingly, statistically, and most strongly, the connection strength was significantly higher around the frontal group although the number of functional connections between neurons was not significantly higher in the frontal group.Connection strength is regarded to be strongly related to response properties to external stimuli (Cossell et al., 2015).It is said that we can classify connection patterns, connecting to the frontal cortex, into multiple modes based on spatial patterns and connecting targets (Gao et al., 2022).Among the patterns, the wiring extending toward the medial side is especially regarded as a mode of connection pattern that supports the default mode network.In addition, the strong functional connections with the deep layer that we found would, in particular, function to strongly spread inputs, brought in via the spatial global wiring pattern, from/to the deep layers within the frontal area.In the near future, the simultaneous recording of local electrical flow in cellular resolution in the frontal region and of global electrical activity spreading along to the global wiring pattern will prove this suggestion more strongly.
The frontal region is also known to be a hub in the extensive network of cortical regions (van den Heuvel and Sporns, 2013;Liska et al., 2015), and also intensely interacts with subcortical regions (Oh et al., 2014).We can offer a possible interpretation of our findings in the context of the current literature.We suggest that the high density of highly active neurons and the strong connection strength in the depths of the network are maintained to serve as an edge (node) in the global network.In particular, we can expect the internal architecture plays an essential role in driving the default mode network observed in the rodent brain (Lu et al., 2012;Stafford et al., 2014;Coletta et al., 2020).
Recently, the relationship between the broad patterns of the default mode network and the cell-by-cell connections in each region have also been discussed (Whitesell et al., 2021).Our findings add scope to this relationship, given from dynamic spikes of living neurons, to elucidate the facts relating with these many other important findings.

E/I balance
Next, interesting trends were observed in the regions labeled dorsal region and ventral region.These regions are more active with a relatively higher firing rate of excitatory cells than other regions.
These trends raise an intriguing hypothesis that these regions may play a role to generate high-firing neural activity in the mouse cortex.The slices labeled dorsal in this study are slightly closer to the occipital part of the top of dorsal side, and are located about halfway between the somatosensory and visual areas.It is known that when moving closer to the visual area from this position, the position becomes a slice that retains connections with subcortical thalamus (MacLean et al., 2006).It is important to note that in our results, the firing rate of excitatory neurons does not increase as one approaches the occipital visual area from the dorsal region.In other words, the higher firing seen in our dorsal area does not reflect the effect of the interaction loop with the thalamus, but rather the property of the internal local circuits.
From our results of E/I balance, we can say that the E/I balance is well maintained in cortical regions as a whole.There is a differential trade-off between speed and specificity in increasing the proportion of excitatory and inhibitory neurons (Sadeh et al., 2015).In this situation, optimal balance of excitatory and inhibitory synapses may allow an asynchronous irregular network to sustain a homeostatic state, which could be re-activated by external stimuli (Vogels et al., 2011).Such an arrangement could enable the system to generate sharp responses, to generate oscillations, and also to achieve optimal control gain and dynamic range (Isaacson and Scanziani, 2011).We used relatively young mice, three weeks old.This age range could reflect their importance in ongoing pattern formation in the process of developing neural circuits (Sadeh and Clopath, 2021).The experimental results in our study are consistent with the fact that, if we observe activities of living neurons as the whole of cortical regions, the contributions of excitatory and inhibitory neurons are highly balanced.At the same time, we need to notice that the E/I balance differs from region to region.How this imbalance helps effective information processes in individual brain regions will be an important future question.

Limitations and future works
As described above, the present study has derived from the data some very interesting trends related to brain nonuniformity, which compensate for information that is not available from information on regional connections and structural cellular distribution previously provided from different recording modalities.However, since the scope of the analysis was limited within the cortex, it will be important in the future to develop the analysis to include subcortical regions as well.In fact, it is known that there are subcortical areas where cell densities are higher than in the cortex (Keller et al., 2018).More analysis of the same cortical data after parcellating with a cutting-edge atlas will also be important in the future to compare with results at more specific brain regions.It is also interesting to contrast the microconnectome obtained by our method with the structural microconnectome, which is obtained using SEM, etc. (Motta et al., 2019).
In fact, providing benchmark data with both structural and activity measurements while keeping the sample's shape unchanged, such as in slices, is crucial for evaluating the accuracy of connection estimation.Sharing this information with readers is essential.It is also important to compare the results with the nonuniformity of genes expressed in the various brain regions (Mouse Genome Sequencing Consortium, 2002;Lein et al., 2007;Fulcher et al., 2019).This study took three years to accumulate more than two data points for individual 16 regional categories from threeto five-week-old mice, allowing us to check for repeatability in each area.Although significance was observed in the trends described above, it is important to increase the number of samples and to compare with data from older mice and compare between three-, four-, and five-week-old mice in the future beyond evaluating common properties within three-to five-week-old mice.However, it should be noted that the statistical significance of the results concerning the connection strength is exceptionally strong, and it is anticipated that the likelihood of significant changes even with an increase in sample size is low.

Final remarks
In any case, there has been no study that systematically measures activity at ms temporal resolution from the whole cortex and discusses its activity and interaction network as in this study.Therefore, we expect the data and findings obtained in this study should be extremely valuable.This study may also be useful for improving future mathematical models of the brain and for advancing the systematic understanding of disease through animal models.
M.S. was supported by several MEXT Grant-in-Aid for Scientific Research (B) (20H04257, 21H01352), Grant-in-Aid for Challenging Research (Pioneering) (23K18493) and the Leading Initiative for Excellent Young Researchers (LEADER) program.

Figure 3 .
Figure 3. Radar charts of age and cortical thickness.a, This panel expresses classification of the brain in 16 categories and their abbreviation names.Table1refers to these definitions of abbreviation names.In the following seven panels, the left hemisphere corresponds to the left half of the circle, and the right hemisphere to the right half.b, This panel summarizes ages of mice used in individual experiments.Lines show the averages of the data within each of the 16 categories.(The left and right hemispheres are expressed with yellow-green and cyan colored lines, respectively.)Black points show the age of each individual mouse used in this experiment.c, represents the thickness of all layers of the cortex, the line is the average value for each angle, and red dots express raw data.In addition to the panel c, panels d-h express the thickness of individual layers(layers 2, 3, 4, 5, 6)  separately.The pie chart regarding layer thickness is represented as a bar graph in Extended Data Figure3-1.The data for cortical thickness are stored in Extended Data Table3-1.

Figure 4 .
Figure 4.The most basic physiological metrics, neuron density, and firing rates.In all panels, features of excitatory and inhibitory neurons are shown as red and blue lines, and individual data samples correspond to dots.Panel a is the radar chart of averaged neuron density included in all layers of the cortical individual brain regions.Panels b-f separately express cell densities of individual layers (layers 2, 3, 4, 5, 6).Panel g summarizes averaged firing rate in all layers of the cortex, and the firing rates of individual layers (layers 2, 3, 4, 5, 6) are separately shown in panels h-l.m, E/I balance calculated as ratio of numbers of active excitatory or inhibitory neurons in the number of all active neurons at individual region groups.The pie chart regarding cell density is represented as a bar graph in Extended Data Figure 4-1.The data for neuron density and neuron count are stored in Extended Data Tables4-1 and 4-2.

Figure 5 .
Figure 5. Basic topological properties at individual brain region groups.In panels a-d, red and blue lines show features of excitatory and inhibitory neurons, respectively.a, Number of inward connections, simply called in-degree.b, Number of outward connections, called out-degree.c, Same radar chart of k-Core centralities at individual brain regions.d, Average FVS of all layers in the cortex.The meanings of colors of lines and dots are the same as Figures 2-4.

Figure 6 .
Figure 6.Interlayer connection strengths.a, Radar chart of outward connection strengths.The strength of the inward connections also shows a similar pattern on the chart.The pie charts related to connection strength are also represented as bar graphs in Extended Data Figure 6-1.b, Sixteen two-dimensional color maps evaluating the connection strength from input layers (horizontal axis) to output layers (vertical axis) are arranged in a circle.Sixteen maps correspond to the angles in Table 1 and many panels in Figures 2-5.When connections between input and output layers are strong (weak), they are colored yellow (blue).The blank figure placed at the center of the circle shows the meaning of the x-and y-axes commonly used in all color maps arranged in a circle, as well as the correspondence between color and intensity.c, This is a color map of p-values obtained when testing the differences in connection strength between regions for all connections outputting from the sixth layer, based on Network-Based Statistics.d, When applying a threshold of p-value 0.05, horizontal lines of low p-values centered around LFV and RFV can be observed.Vertical lines of low p-values from RV are also visible.e, However, in terms of effect size, only the horizontal lines in frontal regions such as LFV, LF, RF, and RFV show high values.The results of the NBS test for the other layers are summarized in Extended Data Figure 6-2.